Question

in a triangle the height is double the base and the area is 400 square cm find the measure of the base and height of the triangle​

Answer 1

Answer:

area is 400 square cm find the measure of

Answer 2

Answer :-

• The base of the triangle = 20 cm.
• The height of the triangle = 40 cm.

To find :-

• The base and height of the triangle.

Solution :-

Let the base of the triangle be "x" cm.

Then :-

• As the height is double the base, it will be "2x" cm.

We know that :-

$\underline{ \boxed{ \sf Area \: of \: a \: triangle = \dfrac{1}{2} \times Base \times Height}}$

Here,

• Area = 400 cm².
• Base = "x" cm.
• Height = "2x" cm.

Substituting the given values in this formula,

$\hookrightarrow\sf400 = \dfrac{1}{2} \times x \times 2x$

$\hookrightarrow\sf400 = \dfrac{1}{2} \times {2x}^{2}$

$\hookrightarrow \sf400 = \dfrac{ {2x}^{2} }{2}$

$\hookrightarrow \sf400 \times 2 = {2x}^{2}$

$\hookrightarrow \sf800 = {2x}^{2}$

$\hookrightarrow \sf\dfrac{800}{2} = x^{2}$

$\hookrightarrow \sf400 = {x}^{2}$

$\hookrightarrow\sf \sqrt{400} = x$

$\hookrightarrow\overline{ \boxed{\sf20 = x}}$

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Hence, the measure of the base and height of the triangle are :-

$\bf Base = x = 20 \: cm.$

$\bf Height = 2x = 2 \times 20 = 40 \: cm.$