Question

In a trapezoid of area 175 cm², the length of two parallel sides are in ratio 3:4. If the height of trapezoid is 10cm, the length of smaller of the two parallel sides is ___________ cm.

2 points

Your anwer​

Answer 1

Given :-

Area of a trapezoid = 175 cm²

Ratio of length of parallel sides = 3:4

Height of the trapezoid = 10 cm

To Find :-

The length of smaller of the two parallel sides.

Solution :-

Let the lengths of the parallel sides be 3x and 4x respectively.

Sum of parallel sides = 3x + 4x = 7x

We know that,

$Area\: of\: a\: trapezoid\: =\: {\dfrac{1}{2}}\: \times\: (sum\: of\: parallel\: sides)\: \times\: height$

On inserting the values in the formula

We get ,

$175\: =\: {\dfrac{1}{2}}\: \times\: 7x\: \times\: 10$

$\implies\: 175\: =\: {\dfrac{1}{\not{2}^{1}}}\: \times\: 7x\: \times\: \not{10}^{5}$

$\implies\: 7x\: =\: {\dfrac{175}{5}}$

$\implies\: 7x\: =\: 35$

$\implies\: x\: =\: {\dfrac{35}{7}}$

$\implies\: x\: =\: \bold{5}$

Length of 1st side = 3x = 3 × 5 = 15 cm

Length of 2nd side = 4x = 4 × 5 = 20 cm

Therefore, length of smaller side is 15 cm

Answer 2

Question

In a trapezoid of area 175 cm², the length of two parallel sides are in ratio 3:4. If the height of trapezoid is 10cm, the length of smaller of the two parallel sides is ___________ cm.

Solution

Area of trapezoid = 175cm²

Height of the trapezoid = 10cm

Let, the parallel sides be 3x and 4x

ATP

$\frac{1}{2} \times (3x + 4x) \times 10 = 175 \\ = ) \: \frac{1}{2} \times 7x \times 10 = 175 \\ = ) \: 35x = 175 \\ = ) \: x = \frac{175}{35} = 5$

Ans:- 1st Parallel side = (3×5)cm = 15cm.

2nd Parallel side = (4×5)cm = 20cm.

Therefore, length of the smaller side is 15cm.