Question

the area of a Trapezium is 138msquare .the distance and the difference between the lengths of the parallel sides are 12m and 7m respectively.find the lengths of the parallel sides​

Answer 1

Answer

The Length of parallel sides are 8m and 15m

Explanation:

Area of the trapezium = 138m²

Distance between parallel sides = Height of the trapezium. So,

Height of the trapezium = 12 m

Difference between parallel sides = 7m

Let One parallel side = x

Other parallel side = x + 7m

Area of trapezium = 1/2 × height × sum of parallel side height

➡ 138m² = 1/2 × 12m × ( x + x + 7m )

➡ 138m² = 6m ( 2x + 7m )

➡ 138m² / 6m = 2x + 7m

➡ 23m = 2x + 7m

➡ 23m - 7m = 2x

➡ 16m = 2x

➡ 16m/2 = x

➡ 8m = x

First parallel side = x = 8m

Second parallel side:

➡ (x + 7m)

➡ 8m + 7m

➡ 15 m

Answer 2

Answer:

The Length of parallel sides are 8m and 15m

Area of the trapezium = 138m²

Distance between parallel sides = Height of the trapezium. So,

Height of the trapezium = 12 m

Difference between parallel sides = 7m

Let One parallel side = x

Other parallel side = x + 7m

$\bold{Area \: of \: trapezium = \frac{1}{2} × height × sum \: of \: parallel \: side \: height}$

$\bold{ 138m² = \frac{1}{2} × 12m × ( x + x + 7m )}$

$\bold{ 138m² = 6m ( 2x + 7m )}$

$\bold{ \frac{138m²}{6m} = 2x + 7m}$

$\bold{23m = 2x + 7m}$

$\bold{ 23m - 7m = 2x}$

$\bold{16m = 2x}$

$\bold{ \frac{16m}{2} = x}$

$\bold{8m = x}$

First parallel side = x = 8m

Second parallel side:

$\bold{(x + 7m) }$

$\bold{8m + 7m}$

$\bold{ \implies \: 15 m}$

Step-by-step explanation:

hope it helps you