Question

the diagonal of a rectangular field is 60 m more than the shorter side if the longer side is 30m
more than the shorter sides find the sides of the field

Answer 1

refer the pic for your respective answer

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

Assume the rectangular field BC = m meters

★Then

AC = (m + 60)

★Then

AB = (m + 30)

${\boxed{\sf\:{Using\;Pythagoras\;theorem}}}$

AC² = BC² + AB²

(m + 60)² = m² + (m + 30)²

m² + 120m + 3600 = m² + m² + 60m + 900

m² - 60m - 2700 = 0

★Factorise the middle term of LHS we get :-

m² - 90m + 30m - 2700 = 0

m(m - 90) + 30(m - 900) = 0

(m + 30)(m - 90) = 0

m + 30 = 0

m = -30

m - 90 = 0

m = 90

●Sides of rectangle can't be in negative

★Hence :-

●Sides of filled are 120m and 90

$\boxed{\begin{minipage}{14 cm} Additional Information \\ \\ \ A\; Quadratic\; Equation\;has\;three\;equal\;roots \\ \\ 1)Real\;and\;Distinct \\ \\ 2)Real\;and\;Coincident \\ \\ 3) Imaginary \\ \\ Note:-Third\; Imaginary\;is\;not\;taken\;in\;class\;10th \\ \\ If\;p(x)\;is\;a\; quadratic\; polynomial\;then\;p(x)=0\;is\;called\; Quadratic\; Polynomial \\ \\ General\;Formula=ax^2+bx+c=0 \\ \\ A polynomial\;whose\;degree\;will\;be\;2\;is\; considered\;as\; Quadratic\; Polynomial \\ \\ Rules\;for\; solving\; Quadratic\; Equations:- \\ \\ Put\;all\;the\;terms\;into\;RHS\;and\;make\it\;zero \\ \\ Substitute\;all\; factors\;equal\;to\;Zero\;Get\;a\;equal\; solution \end{minipage}}$