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Chapter 11: Q29. (page 432)

a. Find the ratio of the areas of鈻�QRTand鈻�QTS.

b. If the area of鈻�QRSis240. Find the length of the altitude from sto.QR鈫�

Short Answer

Expert verified

a.The ratio of the areas of 鈻�QRTand 鈻�QTSis2:3.

b. The altitude from s toQR is 240.

Step by step solution

01

Step 1. Given information.

QR=24,RT=12andTS=18

02

Step 2. Concept Used.

Area of triangle can be found using the formula

A=12bh

Whereb= base of triangle andh= height of triangle.

03

Step 3. Find the area of triangles.

Area of triangle鈻�QRTis

b=RT=12h=hA=12bhA=12(12)(h)A(QRT)=6h

Area of triangle鈻�QTSis

b=TS=18h=hA=12bhA=12(18)(h)A(QTS)=9h

04

Step 4. Find the ratio of areas.

So, the ratio of the areas of鈻�QRTand鈻�QTSwill be

A(螖QRT)A(螖QTS)=6h9h=23=2:3

Therefore, the ratio of the areas of 鈻�QRTand 鈻�QTSis 2:3.

05

Step 1. Given information.

Area of鈻�QRS=240

Let the altitude be x

06

Step 2. Concept Used.

Area of triangle can be found using the formula

A=12bh

Where b= base of triangle and h=height of triangle.

07

Step 3. Use the formula of the area of triangle.

b=QR=24h=xA=12bhA=12(24)(x)A(QRS)=12x240=12xx=20

Therefore, the altitude from s to QRis 20.

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Most popular questions from this chapter

  1. Suppose you have40mof fencing with which with to make a rectangle pen for a dog. If one side of the rectangle is xlong, explain why the other side is(20鈭�x)mlong.

a. Use the diagram at the right. Find the area of鈻�PQRS.

b. Use the diagram at the right. Find the area of鈻�PSR.

c. Use the diagram at the right. Find the area of鈻�OSR. (Hint: Refer to鈻�PSR and use Exercise28).

d. Use the diagram at the right. What is the area of鈻�PSO?

e. Use the diagram at the right. What must the area of鈻�POQbe? Why? What must the area of鈻�OQR be?

f. Use the diagram at the right. State what you have shown in parts (a)-(e) about how the diagonals of a parallelogram divide the parallelogram.

The base of a rectangle is(k+7)and perimeter(4k+20). What is the area and height of the rectangle?

The base of a rectangle is(a+3) and height(a鈭�3) . What is the area and perimeter of the rectangle?

a. What is the converse of the Area Congruence Postulate?
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