Answer:
Base = 10.4 inches
Height = 5.4 inches
Step-by-step explanation:
Let the length of the base = x
The height of the triangle = x - 5
Area of the triangle = 52
;Area of a triangle = 1/2 × base × height
; 52 = [x(x - 5)]/2
; 104 = x^2 - 5
;Where x = square root of (104 + 5)
; x = 10.4
;The base(x) = 10.4 in
;The height (x - 5) = 10.4 - 5
= 5.4 in
The base is 13 inches and the height is 8 inches.
The area of the triangle is given by;
[tex]\rm Area \ of \ triangle=\dfrac{1}{2} \times Height \times Base[/tex]
The height of a triangle is five inches less than the length of its base, and if the area of the triangle is 52 square inches.
Let the length of the base is x and the height of the triangle = x - 5.
Substitute all the values in the formula
[tex]\rm Area \ of \ triangle=\dfrac{1}{2} \times Height \times Base\\\\52=\dfrac{1}{2}\times x \times (x-5)\\\\ 52 \times 2=x(x-5)\\\\104 =x^2-5x\\\\x^2-5x-104=0\\\\x=\dfrac{-(-5)\pm\sqrt{(-5)^2-4\times 1\times -104} }{2\times 1}\\\\x=\dfrac{-(-5)\pm\sqrt{25+416} }{2}\\\\x=\dfrac{5\pm\sqrt{441} }{2}\\\\x =\dfrac{5+21}{2}, \ \dfrac{5-21}{2}\\\\x =\dfrac{26}{2}, \ \dfrac{-16}{2}\\\\x= 13, \ -8[/tex]
The length of the base is x = 13, and the height of the triangle = x - 5 = 13-5 = 8.
Hence, the base is 13 inches and the height is 8 inches.
Learn more about triangles here;
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