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asambeis [7]
3 years ago
11

an isosceles triangle has congruent sides of 20cm. the base is 10cm. find the height of the triangle.​

Mathematics
1 answer:
dolphi86 [110]3 years ago
8 0

Answer:

\large\boxed{A_\triangle=25\sqrt{15}\ cm^2}

Step-by-step explanation:

Look at the picture.

The formula of an area of a triangle:

A_\triangle=\dfrac{bh}{2}

<em>b</em><em> - base</em>

<em>h</em><em> - height</em>

<em />

We need a length of a height.

Use the Pythagorean theorem:

leg^2+leg^2=hypotenuse^2

We have:

leg=5,\ leg=h,\ hypotenuse=20

Substitute:

5^2+h^2=20^2

25+h^2=400             <em>subtract 25 from both sides</em>

h^2=375\to h=\sqrt{375}\\\\h=\sqrt{(25)(15)}\\\\h=\sqrt{25}\cdot\sqrt{15}\\\\h=5\sqrt{15}\ cm

Calculate the area:

A_\triangle=\dfrac{(10)(5\sqrt{15})}{2}=\dfrac{50\sqrt{15}}{2}=25\sqrt{15}\ cm^2

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