Question

The difference of the parallel sides of a trapezoidal field is 20 m. Its area is 450 m² and its altitude is 15m Find the length of the parallel sides.​

Answer 1

Answer:

The length of the parallel sides are 20 m and 40 m

Step-by-step explanation:

we know that

The area of a trapezoid is equal to

$A=\frac{1}{2}[b_1+b_2]h$

where

A is the area

b_1 and b_2 are the parallel sides

h is the altitude

we have

$A=450\ m^2\\h=15\ m$

substitute

$450=\frac{1}{2}[b_1+b_2](15)$

$b_1+b_2=60$ -----> equation a

Remember that

The difference of the parallel sides of a trapezoidal field is 20 m

I will assume that

$b_1 >b_2$

so

$b_1-b_2=20$ ----> equation b

solve the system of equations a and b by elimination

Adds equation a and equation b

$b_1+b_2=60\\b_1-b_2=20\\-------------\\b_1+b_1=60+20\\2b_1=80\\b_1=40\ m$

Find the value of b_2

$b_1+b_2=60$

substitute the given value

$40+b_2=60$

$b_2=20\ m$

therefore

The length of the parallel sides are 20 m and 40 m