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soldi70 [24.7K]
3 years ago
10

The base of a triangle is seven less than twice its height. If the area of the triangle is 100cm^2 find the length of the base

Mathematics
2 answers:
shusha [124]3 years ago
8 0
Okay i got lets work itAnswer:

<span>h≈4.874</span> <span>cm,b≈21.748</span> cm

Explanation:

<span><span>Atriangle</span>=<span>12</span>bh</span>

"The base of a triangle is twelve more than twice its height."

From this we can say that:

<span>b=<span>2h</span>+12</span>

So, if <span>A=<span>12</span>bh</span>, we can replace b with <span>2h+12</span>.

<span>A=<span>12</span><span>(2h+12)</span>h</span>

<span>53=<span>12</span><span>(2h+12)</span>h</span>

<span>53=<span>(h+6)</span>h</span>

<span>53=<span>h2</span>+6h</span>

<span><span>h2</span>+6h−53=0</span>

Use the quadratic formula.

<span>h=<span><span>−6±<span>√<span><span>62</span>−4<span>(−53)</span><span>(1)</span></span></span></span>2</span></span>

<span>h≈4.874</span>

(Ignore the negative answer—height can't be negative.)

<span>b≈2<span>(4.874)</span>+12</span>

<span>b≈<span>21.748
</span></span>

Alexeev081 [22]3 years ago
7 0
2x-7 * x
----------- =. 100^2= 10000 
     2


2x^2-7/2= x^2-7/2

x^2-7/2=10000

x^2 = 20007/7
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