Mathematics: In the two similar trapezoids below, he = 20, what is da? a. 10 b. 20 c. 30 d. 40

Y=mx+bm=slopeparalell lines have the same slopey=1/2x+3m=slope=1/2the slope of the paralelll line is 1/2...

In the two similar trapezoids below, he = 20, what - id203717757, tryintopassenioryear

theojw

09.01.2022

DA = 30

Step-by-step explanation:

Given : the two trapezoid AFGH and ABCD are similar.

We have to find the value of DA , given HE =20

Two figures are said to be similar if their corresponding sides are in same ratios.

The two given trapezoid AFGH and ABCD are similar.

Then their corresponding sides are in same ratios that is

$\frac{HE}{DA}=\frac{HG}{DC}=\frac{GF}{CB}=\frac{EF}{AB}$

Substitute the values for given sides , we have,

$\frac{20}{DA}=\frac{56}{42x}=\frac{10x}{30}=\frac{EF}{70}$ .....(1)

Now , first we find the value of x,

Comparing second and third ratio, we have,

$\frac{56}{42x}=\frac{10x}{30}$

Cross multiply, we get

$56 \cdot 30=10x\cdot 42x$

Simplify for x, we have,

56=14x^2

x^2=4

Thus, x = 2 as x can not be negative.

Then (1) becomes,

$\frac{20}{DA}=\frac{56}{84}=\frac{20}{30}=\frac{EF}{70}$

Comparing first and third ratio, we get,

$\frac{20}{DA}=\frac{20}{30}$

Now solve for DA,

we get DA = 30

Thus, DA = 30

0,0(0 оценок)