Question:- Find X
Given:-
- A rectangle consist of 4 identical triangle
- diagonals of rectangle are at 90° to each other
- length of half of the one diagonal is 8 in
- length of the half of the other diagonal is X in
- Area of the rectangle = 48 in²
- Base of triangle = 8in
- height of the triangle = x in
Answer :- X = 3 in
Formula :- Area of the rectangle is equal to the sum of the area of the all four the triangle
[tex]area \: of \: rectangle \\= 4 \times area \: of \:identical \: triangle[/tex]
Explanation :-
[tex]area \: of \: rectangle =\\ 4 \times area \: of \:identical \: triangle[/tex]
[tex]48 {in}^{2} = 4 \times \frac{1}{2} \times base \times height \\ 48 {in}^{2} = 2 \times base \times height \\ \frac{48}{2} = 8 \times height \\ \frac{ \cancel{48} {}^{ \: \: 24} }{ \cancel{2}} = 8 \times height \\ \frac{24}{8} = height \\ \frac{ \cancel{24} {}^{ \: \: 3} }{ \cancel{8}} = height \: \\ height = x = 3in \: [/tex]
