Question

The front of a house is in the shape of an equilateral triangle with the measure of one side is 10m. Find the height of the house.​

Answer 1

$\huge\fcolorbox{black}{lime}{AnsweR:}$

The triangle is 10m on each side.

Set x = height.

Using Pythagorean theoremx^2 + (5 which is is 1/2 of the base)^2

= 10^2 x^2 + 5^2

= 10^2x^2 + 25

= 100subtract 25 from each sidex^2

= 75x

= sqrt(75)

= 8.66m.

Answer 2

$\mathfrak \red{Question :-}$

$\sf{The \: front \: of \: a \: house \: is \: in \: the \: shape \: of \: an}$$\sf{equilateral \: triangle \: with \: the \: measure \: of \: one \: side}$$\sf{is \: 10m. \: Find \: the \: height \: of \: the \: house.}$

$\mathfrak \red {Solution :-}$

$\sf{The \: triangle \: is \: 10m \: on \: each \: side.}$$\sf{set \: x = height}$

$\sf{Using \: Pythagorean \: theorem}$

$\sf{x^2 + (5 \: which \: is \: 1/2 \: of \: the \: base)^2 = 10^2}$

$\sf{x^2 + 5^2 = 10^2}$

$\sf{x^2 + 25 = 100}$

$\sf{subtract \: 25 \: from \: each \: side}$

$\sf{x^2 = 75}$

$\sf\purple{x = \sqrt{75} ) = 8.66m}$