Mathematics Question and Solution
Calculating h.
Let x be the two equal lengths.
a = x+x
a = 2x units.
a is the base of the ascribed right-angled triangle.
b²+24² = a²
b² = (2x)²-24²
b = √(4x²-576) units.
c = b-7
c = (√(4x²-576)-7) units.
Calculating x.
√(4x²-576) ~ x
2x ~ (√(4x²-576)-7)
Cross Multiply.
2x² = √(4x²-576)²-7√(4x²-576)
7√(4x²-576) = 2x²-576
49(4x²-576) = 4x⁴-2304x²+331776
196x²-28224 = 4x⁴-2304x²+331776
4x⁴-2500x²+360000 = 0
x⁴-625x²+90000 = 0
Therefore;
x ≠ 15 units.
x = 20 units.
Recall.
c = (√(4x²-576)-7) units.
And x = 20 units.
c = √(4*20²-576)-7
c = 25 units.
It implies, length h is;
h²+x² = c²
h² = c²-x²
h² = 25²-20²
h = √(625-400)
h = √(225)
h = 15 units.
