To construct the roof of a house, an architect must determine the measures of the support beams of the roof.

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1 Metric Relations Practice Name : 1 To construct the roof of a house, an architect must determine the measures of the support beams of the roof. m = 6 m m = 8 m m = 10 m What is the length of segment F? F In rectangle shown below, line segment is perpendicular to diagonal. In addition, m = 9 cm and m = 15 cm. What is the length of diagonal? The length of diagonal is cm.

2 3 Louise wants to buy the piece of land corresponding to triangle shown in the rectangle below. 30 m 40 m What is the area of this piece of land? Show your work. 4 In the figure to the right, triangle is right-angled at and is an altitude. m = 15 cm and m = 1 cm. What is the perimeter of triangle? Show your work.

3 5 kennel is the shape of a square topped by an isosceles right triangle, as shown in the adjacent sketch. ach congruent side of the triangular roof measures 1 metre. The roof extends 0. metres over each side of the kennel. 0. m H 0. m What is the full height of the kennel? Show your work. Work 0. m H 0. m nswer : The full height of the kennel is m.

4 6 is a right triangle in which segment measures 10 cm and segment, 5 cm. 10 cm 5 cm What is the measure of segment, to the nearest tenth? 7 is a right triangle in which segment measures 5 cm and segment, 10 cm. 5 cm 10 cm What is the measure of segment, to the nearest tenth?

5 8 two-sided shelter is supported by vertical posts. The diagram below represents one end of this shelter. Posts.5 m 10 m Using the information given in the diagram, calculate the length of side. 9 Given triangle with a right angle at. is drawn perpendicular to at and is drawn perpendicular to at. The height measures 1 cm, hypotenuse measures 5 cm and side measures 0 cm. Find the measure of.

6 10 In right-angled triangle below, altitude coincides with a diagonal of rectangle F. F Line segments and measure 16 m and 9 m respectively. Rounded to the nearest tenth, what is the perimeter of rectangle F? Show your work. 11 In the following figure, is a right triangle. m F = 5 cm m = cm F cm F 5 cm F What is the area of triangle F? Show all your work.

7 1 nswers 3.60 m The length of diagonal is 5 cm m 40 m Measure of segment m = (m ) + (m ) = m = 50 m m Pythagorean theorem Measure of segment m m = = m = m m 50 m 4 m In a right triangle, the product of the measures of the legs is equal to the product of the measures of the hypotenuse and the altitude drawn to the hypotenuse. Measure of segment m = (m ) = 30 m =18 m 4 m (m ) Pythagorean theorem rea of triangle m m rea = 18 4 rea = rea = 16 m Result : The area of the piece of land is 16 m.

8 4 Measure of m = 15 1 = 9 Measure of Measure of m m = m m m = m 15 = 1 9 m = ( 7.) = 9. 6 = 7. Perimeter of triangle : = 8.8 Result : The perimeter of triangle is 8.8 cm. 5 Measure the roof s base, ( m ) = m 1.41 Measure of one side of square = m H 0. m Height H of roof m m = m m H m H m H 0.71 Full height of kennel = 1.7 nswer : The full height of the kennel is 1.7 m cm 8 (m ) = m m (m ) =10 1,5 (m ) =15 m = 5 5 m 11. m Result : m = 5 5 m or m 11. m.

9 9 In right triangle, we apply the Pythagorean relation. (m ) = (m ) + (m ) 0 = 1 + m m =16 c h a) Right angles. b) ngles common to both triangles c) Δ ~ Δ Two triangles are similar if they have two corresponding angles congruent. In two similar triangles, the corresponding sides are proportional. m m = m m m 1 = m = = Result : 9.6 cm. 10 Measure of segment (m ) = m m m = 1 In a right triangle, the altitude from the hypotenuse is the proportional mean between the two segments it determines on the hypotenuse. m = (m ) = + (m ) =15 Pythagorean theorem m m = m m 16 9 =15 m m = = 7. In a right-angled triangle, the product of the measures of the legs is equal to the product of the measures of the hypotenuse and the altitude drawn to the hypotenuse. m = (m ) (m ) = 1 7. = 9.6 Pythagorean theorem Perimeter of rectangle F P = m + m = = = 33.6 Result : Rounded to the nearest tenth, the perimeter of rectangle F is 33.6 m.

10 11 alculate m F ( m F) ( m ) = m F 5 1 = m F = m F alculate m M m = ( m F) m = 1 m = 1 = 10.5 rea of triangle F m m F 10.5 = nswer The area of triangle F is 4.06 cm.

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