Question

The area of a parallelogram is 507 cm2. Its height is three times its base. Find the height and base.

Select one:
a. b=15cm h=45cm
b. b=13cm, h=39 cm
c. b=14cm h=42cm

Answer 1

The height and base is b) 13cm & h = 39cm

Step-by-step explanation:

Given:

area of parallelogram = 507 sq.cm

height of the parallelogram is 3 times its base

To find:

height and base of the parallelogram

Solution:

Let's assume the base of the parallelogram is x cm

Then, according to the condition, the height is 3 times its base

∴ height of the parallelogram = 3x cm

Now, area of parallelogram = b X h

∴  Area of parallelogram = x (3x)

∴  Area of parallelogram = 3x²

But the area is given as 507 sq cm

∴  507 = 3x²

∴  3x²= 507

∴  x²= 507/3

∴  x²= 169

Taking square roots

∴ x = √169

∴ x = ±13

But the length cannot be negative

∴ x = 13 cm

Thus, base = 13cm

Now, height = 3 times the base

∴ height = 3 X 13

∴ height = 39cm

Thus, the base and height of the parallelogram are 13cm & 39cm respectively

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Answer 2

Answer:

The base of the parallelogram is 13 cm and the height of the parallelogram is 39 cm

Step-by-step explanation:

Given:

The area of a parallelogram is 507 cm2.

Its height is three times its base.

To find: The base and height of the parallelogram

Solution:

Parellelogram:

• A quadrilateral with two sets of parallel sides is referred to as a parallelogram.
• In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size.
• Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the total of all interior angles.

Given that

The area of a parallelogram is 507 cm2.

Its height is three times its base

Let the height of the parallelogram = 3x cm

then the base of the parallelogram = x cm

Area of the parallelogram = 507 cm²

Area of parallelogram = base × height

                  507  = x × 3x

⇒ 507 = $3x^{2}$

⇒ $x^{2} = \frac{507}{3}$

⇒$x^{2} = 169$

⇒ x = 13

Therefore 3 x = 3 × 13

                      = 39

Base = 13 cm

Height = 39 cm

Final answer:

The base of the parallelogram is 13 cm and the height of the parallelogram is 39 cm

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