Question

The height of a parallelogram is 6 feet more than its base. If the area of the parallelogram is 160 square feet, find the length of its base

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Length\:of\:base=10\:feet}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given:}} \\ \tt: \implies Height \: of \: parallelogram = 6 \: feet \: more \: than \: its \: base \\ \\ \tt: \implies Area \: of \: parallelogram = 160 \: square \: feet \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Length \: of \: base = ?$

• According to given question :

$\tt\circ \:Let \: length \: of \: base \: be \: x \: feet \\ \\ \tt\circ \: \: Height \: of \: parallelogram = (x + 6)feet\\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Area \: of \: parallelogram = Base \times Height \\ \\ \tt: \implies 160 = x \times (x + 6)\\ \\ \tt : \implies 160 = {x}^{2} + 6x \\ \\ \tt: \implies {x}^{2} + 6x - 160 = 0 \\ \\ \bold{Solving \:by \: middle \: term \: spiliting} \\ \tt: \implies {x}^{2} + 16x - 10x - 160 = 0 \\ \\ \tt: \implies x(x + 16) - 10(x + 16) = 0 \\ \\ \tt: \implies ( x + 16)(x - 10) = 0 \\ \\ \green{\tt: \implies x = 10 } \\ \\ \bold{NOTE- We \: cant \: take \: negative \: values} \\ \\ \green{\tt{\therefore Length \: of \: base = 10 \: feet}}$

Answer 2

Answer:

$\large\boxed{\sf{10\;\;ft.}}$

Step-by-step explanation:

It's being given that there is a paralleolgram.

Let the length of its base is x ft.

Therefore, length of height = (x+6) ft.

Also, area of paralleolgram = 160 sq. ft.

Now, we know that,

Area of paralleolgram = base × height

Therefore, we will get,

$= > x(x + 6) = 160 \\ \\ = > {x}^{2} + 6x - 160 = 0 \\ \\ = > {x}^{2} + 16x - 10x - 160 = 0 \\ \\ = > x(x + 16) - 10(x + 16) = 0 \\ \\ = > (x + 16)(x - 10) = 0 \\ \\ = > x + 16 = 0 \: \: \: \: \: or \: \: \: \: \: x - 10 = 0 \\ \\ = > x = - 16 \: \: \: \: \: or \: \: \: \: \: x = 10$

But, we know that, length can't ever be negative.

Therefore, x = 10

Hence, length of base = 10 ft.