the length of a rectangle exceed its breadth by 4cm.if length and breadth are incresed by 3cm the aera of the new reactangle will be 81cm more then that of the given reactngle.then
a)length of the given rectangle is?
b)breath of the given rectangle is?
c)area of new angle is?
now: w and w+4, area = w(w+4)
after growth, we have
(w+3)(w+4+3) = w(w+3)+81
w^2+10w+21 = w^2+3w+81
7w = 60
w = 60/7
Now you can figure all the dimensions.
To solve this problem, let's follow these steps:
Step 1: Set up equations based on the given information.
Let's assume that the length of the given rectangle is L cm, and the breadth is B cm.
According to the first statement, the length of the rectangle exceeds its breadth by 4 cm. Therefore, we can write the equation: L = B + 4.
According to the second statement, when both the length and breadth are increased by 3 cm, the area of the new rectangle (let's call it A1) will be 81 cm² greater than the area of the given rectangle (let's call it A0). So we can write the equation: A1 = A0 + 81.
Step 2: Find the area of the given rectangle.
The area of a rectangle is given by the formula A = L × B. So the area of the given rectangle is A0 = L × B.
Step 3: Substitute values and solve the equations.
Now, let's substitute the value of L from the first equation into the second equation:
(L + 3)(B + 3) = L × B + 81.
Next, we can substitute the value of L in terms of B from the first equation into the equation for A0 to get:
A0 = (B + 4) × B.
Step 4: Solve the equations.
Expanding and simplifying the equation (L + 3)(B + 3) = L × B + 81, we get:
LB + 3L + 3B + 9 = LB + 81.
Simplifying further, we can cancel out the LB terms and rearrange the equation to isolate L:
3L + 3B = 72.
From the first equation (L = B + 4), we can substitute the value of L in terms of B into the equation 3L + 3B = 72:
3(B + 4) + 3B = 72.
Simplifying the equation, we get:
6B + 12 = 72,
6B = 60,
B = 10.
Therefore, the breadth of the given rectangle is 10 cm.
To find the length of the given rectangle, we can substitute the value of B into the equation L = B + 4:
L = 10 + 4,
L = 14.
Therefore, the length of the given rectangle is 14 cm.
Finally, to find the area of the new rectangle (A1), we can substitute the values of L and B into the equation (L + 3)(B + 3):
A1 = (14 + 3)(10 + 3),
A1 = 17 × 13,
A1 = 221 cm².
Hence, the area of the new rectangle is 221 cm².