Question

the height of parallelogram is twice its base if its area is 450 square find its base and height​

Answer 1

$\huge\bf\underline{Answer}$

Given :-

• Height of the Parallelogram is twice of its base

• Area of the Parallelogram = 450cm²

To Find :-

• Height of the Parallelogram

• Base of the Parallelogram

Solution :-

Let the base of the Parallelogram be x

Then the height of the Parallelogram be 2x

Formula :-

⠀⠀$\boxed{\large\sf {Area \: of \: the \: Parallelogram = B × H}}$

where,

• B = Breadth of the Parallelogram

• H = Height of the Parallelogram

By substituting values according to the formula,

$\sf{:⇒2x \: \times x = 450 {cm}^{2} }$

$\sf{:⇒ {2x}^{2} = 450 {cm}^{2} }$

$\sf{:⇒ {x}^{2} = \dfrac{450}{2} }$

$\sf{:⇒ {x}^{2} = 225}$

$\sf{:⇒x = \sqrt{225} }$

$\sf{:⇒x = 15cm}$

Hence, The required measurements are,

Base of the Parallelogram = x = 15cm

Height of the Parallelogram = 2x = 2 × 15cm = 30cm

Let's verify :-

Area of the Parallelogram = B × H

450cm² = 15cm × 30cm

450cm² ⇔ 450cm²

Hence, Verified

Answer 2

Answer:

Given :-

• The height of the parallelogram is twice its base of its area is 450 cm².

To Find :-

• What is the base and height.

Formula Used :-

${\purple{\boxed{\large{\bold{Area\: of\: parallelogram\: =\: Base\: \times Height}}}}}$

Solution :-

Let, the base be x

And, the height will be 2x

According to the question by using the formula we get,

⇒ $\sf 450 =\: x \times 2x$

⇒ $\sf 450 =\: 2{x}^{2}$

⇒ $\sf \dfrac{\cancel{450}}{\cancel{2}} =\: {x}^{2}$

⇒ $\sf 225 =\: {x}^{2}$

⇒ $\sf \sqrt{225} =\: x$

⇒ $\sf 15 =\: x$

➠ $\sf\bold{\green{x =\: 15\: cm}}$

Hence, the required base and height are,

✧ Base = x = 15 cm

✧ Height = 2x = 2(15) = 30 cm

$\therefore$ The base and height of the parallelogram is 15 cm and 30 cm respectively.

VERIFICATION :-

↦ $\sf 450 =\: x \times 2x$

By putting x = 15 we get,

↦ $\sf 450 =\: 15 \times 2(15)$

↦ $\sf 450 =\: 15 \times 30$

↦ $\sf 450 =\: 450$

➦ LHS = RHS

Hence, Verified ✔