Question

2
5. The area of a parallelogram is
128 cm and its altitude is twice the
corresponding base. What is the
length of the base ?
(A) 6 cm
(B) 7 cm
(C) 12 cm
(D) 8 cm​

Answer 1

Given :

• Area of Parallelogram is 128 cm² .
• Altitude/Height of //gm is twice its base .

To Find :

• Base of Parallelogram .

Solution :

$\longmapsto\tt{Let\:base\:be=x}$

As Given that Height of parallelogram is twice its base . So ,

$\longmapsto\tt{Height=2x}$

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Parallelogram=b\times{h}}$

Putting Values :

$\longmapsto\tt{128=x\times{2x}}$

$\longmapsto\tt{128=2{x}^{2}}$

$\longmapsto\tt{\cancel\dfrac{128}{2}={x}^{2}}$

$\longmapsto\tt{64={x}^{2}}$

$\longmapsto\tt{\sqrt{64}=x}$

$\longmapsto\tt\bf{8\:cm=x}$

So , The Length of the base is 8 cm .

Option d) 8 cm is Correct .

Answer 2

Given :-

Area = 128 cm²

To Find :-

Length of base

Solution :-

Let the base be b

Altitude be a

So,

Altitude is twice than base

a = 2b

Now

Area = a × b

128 = a × b

Putting b = 2a

128 = a × 2a

128 = 2a²

128/2 = a²

64 = a²

√64 = a

8 = a

Length of base = 8 cm

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