Question

Given expressions are for Area of rectangle (A) and Volume of cuboid (V) respectively : Find their dimensions. A = (20m2 – 48m + 16) , V = (5x3 – 125x)
Can anyone help me with this question.Full explanation.No irrevelent answers.If the answer is correct I will surely mark as brainlest​

Answer 1

$\Large{\underline{\underline{\bold{☆Given:}}}}$

• Area of Rectangle → A = 20m²-48m+16
• Volume of Cuboid → V = 5x³-125x

$\Large{\underline{\underline{\red{\bold{➸To\;Find:}}}}}$

• Dimensions of Rectangle and Cuboid.

$\Large{\underline{\underline{\bold{\color{salmon}๛Required\; Response:}}}}$

✧Rectangle:-

• $\pink{\bf{Area\;of\; rectangle = Length×Breadth}}$

$20 {m}^{2} - 48m + 16 \\ 20 {m}^{2} - 40m - 8m + 16 \\ 20m(m - 2) - 8(m - 2) \\ (20m - 8)(m - 2) \\ m = \frac{8}{20} \: (or) \: 2$

The Roots of the QE are $\bold{m =\frac{8}{20}\;\&\;2}$

If at all the length of the rectangle is (20m-8) then the breadth will be (m-2), or else vise versa.

Dimensions of Rectangle

• ☞ $\Large{\boxed{\blue{\bold{(20m-8)\&(m-2)}}}}$

✧Cuboid:-

• $\pink{\bf{Volume\;of\; Cuboid = Length×Breadth×Height}}$

$5 {x}^{3} - 125x \\ 5x( {x}^{2} - 25) \\ 5x(x^{2} - {5}^{2} ) \\ 5x(x + 5)(x - 5) \\ (5x) \times (x + 5) \times (x - 5)$

Dimensions of Cuboid

• ☞ $\Large{\boxed{\blue{\bold{5x,(x+5)\;\&\;(x-5)}}}}$

➸ ɱσɾε ƭσ ℓεαɾɳ:-

▽Rectangle:- The Quadrilateral in which all angles measure 90° and opposite sides are equal is called Rectangle.

• → Perimeter of Rectangle = 2(l+b)

▽Cubiod:- A 3 dimensioned figure which has a rectangular face and 90° to each other and with six faces whose polyhedra graph is same as that a cube.

• → Total Surface Area of Cuboid = 2(lb+bh+hl)
• → Lateral Surface Area of Cuboid = 2h(l+b)

$\boxed{\tt{@Mr Sovereign}}$

Hope This Helps!!

Answer 2

Answer :-

• Rectangle:-

$\pink{\bf{Area\;of\; rectangle = Length×Breadth}}$

$20 {m}^{2} - 48m + 16 \\ 20 {m}^{2} - 40m - 8m + 16 \\ 20m(m - 2) - 8(m - 2) \\ (20m - 8)(m - 2) \\ m = \frac{8}{20} \: (or) \: 2$

The Roots of the QE are $\bold{m =\frac{8}{20}\;\&\;2}$

If at all the length of the rectangle is (20m-8) then the breadth will be (m-2), or else vise versa.

• Dimensions of Rectangle :-

$\leadsto$ $\Large{\boxed{\blue{\bold{(20m-8)\&(m-2)}}}}$

• Cuboid:-

$\pink{\bf{Volume\;of\; Cuboid = Length×Breadth×Height}}$

$5 {x}^{3} - 125x \\ 5x( {x}^{2} - 25) \\ 5x(x^{2} - {5}^{2} ) \\ 5x(x + 5)(x - 5) \\ (5x) \times (x + 5) \times (x - 5)$

• Dimensions of Cuboid :-

$\leadsto$ $\Large{\boxed{\blue{\bold{5x,(x+5)\;\&\;(x-5)}}}}$

★ More Information :-

• Rectangle:- The Quadrilateral in which all angles measure 90° and opposite sides are equal is called Rectangle.

$\mapsto$ Perimeter of Rectangle = 2(l+b)

• Cubiod:- A 3 dimensioned figure which has a rectangular face and 90° to each other and with six faces whose polyhedra graph is same as that a cube.

$\mapsto$ Total Surface Area of Cuboid = 2(lb+bh+hl)

$\mapsto$ Lateral Surface Area of Cuboid = 2h(l+b)