Problem solving

Question

Magtalas01Tyro

Asked: March 31, 20212021-03-31T14:45:17+00:00 2021-03-31T14:45:17+00:00In: High School/Senior Secondary School, Statistics and Probability

Find the base and the height of a triangle with area of 49 square inches if the height is 7 inches less than the length of its base.

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acedstud · Accepted Answer · 2021-03-31T16:14:26+00:00

Best Answer

acedstud

The area (A) of a triangle is given by $A=\dfrac{1}{2}bh$ , where $b$ is the length of the base and $h$ is the height.

Here $A=49$ square inches and $h=b-7$ inches.

Thus, $49=\dfrac{1}{2}b(b-7)$

Multiplying both sides by 2 gives $b^2-7b=98\Rightarrow b^2-7b-98=0$

$\Rightarrow(b-14)(b+7)=0$

$\Rightarrow b-14=0$ or $b+7=0$

$\Rightarrow b=14$ or $b=-7$

But b is a length and has to be positive so $b=14$ .

Therefore, the base is 14 inches and the height is 14 – 7 = 7 inches.

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