Question

. A rectangular garden will be divided into two plots by fencing it on the diagonal. The diagonal distance from one corner of the garden to the opposite corner is five yards longer than the width of the garden. The length of the garden is three times the width. Find the length of the diagonal of the garden.

Answer 1

Answer:

Step-by-step explanation:

The width = x

The length of the garden is three times the width => the length = 3x

The diagonal distance is five yards longer than the width=> the width=x+5

pythagorean theorem:

$(x+5)^{2} = 3x^{2} +x^{2} \\=> x +5 = \sqrt{( 3x)^{2} +x^{2}} \\=> x+5= \sqrt{10x^{2} } \\=>x+5= \sqrt{10} x\\=> \sqrt{10} x - x=5\\=> x= \frac{5+5\sqrt{10} }{9} (yd)\\\\ the diagonal = x+5 = \frac{5+5\sqrt{10} }{9} +5= \frac{50+5\sqrt{10} }{9} (yd)$

My English is not too good but I hope you will understand.